Numbers-19 (XAT-2011) (Data Sufficiency)

The question is followed by two statements labelled as I and II. Decide if these statements are sufficient to conclusively answer the question. Choose the appropriate answer from the options given below:

A. Statement I alone is sufficient to answer the question.

B. Statement II alone is sufficient to answer the question.

C. Statement I and statement II together are sufficient, but neither of the two alone is sufficient to answer the question.

D. Either statement I or statement II alone is sufficient to answer the question.

E. Neither statement I nor statement II is necessary to answer the question.

Q) Given below is an equation where the letters represent digits.

(PQ).(RQ) = XXX. Determine the sum of P+Q+R+X                            (3 Marks)

I.                    X=9

II.                  The digits are unique

Solution follows here:

Solution:

It’s a trickier one. Observe that, the number XXX shall be represented as product of two two-digit numbers with unit digit being same. Now let us check all the options available for XXX:

For X = 1, 111 = 3*37, which cannot be represented in the form (PQ).(RQ)

For X = 2, 222 = 6*37, which cannot be represented in the form (PQ).(RQ)

For X = 3, 333 = 9*37, which cannot be represented in the form (PQ).(RQ)

For X = 4, 444 = 12*37, which cannot be represented in the form (PQ).(RQ)

For X = 5, 555 = 15*37, which cannot be represented in the form (PQ).(RQ)

For X = 6, 666 = 18*37, which cannot be represented in the form (PQ).(RQ)

For X = 7, 777 = 21*37, which cannot be represented in the form (PQ).(RQ)

For X = 8, 888 = 24*37, which cannot be represented in the form (PQ).(RQ)

For X = 9, 999 = 27*37, which only can be represented in the form (PQ).(RQ)

Where P = 2, Q = 7, R = 3 (OR) P = 3, Q = 7, R = 2

=> P+Q+R+X = 2+7+3+9 = 21

“As a unique situation is resulted leaving out all other options, the problem can be calculated with no other additional data”

Answer (E)